1. Field of the Invention (Technical Field)
The present invention relates to control system design methods.
2. Description of Related Art
Note that the following discussion refers to a number of publications by author(s) and year of publication, and that due to recent publication dates certain publications are not to be considered as prior art vis-a-vis the present invention. Discussion of such publications herein is given for more complete background and is not to be construed as an admission that such publications are prior art for patentability determination purposes.
Today's engineering systems sustain desirable performance by using well-designed control systems based on fundamental principles and mathematics. Many engineering breakthroughs and improvements in sensing and computation have helped to advance the field. Control systems currently play critical roles in many areas, including manufacturing, electronics, communications, transportation, computers, and networks, as well as many commercial and military systems. Traditionally, almost all modern control design is based on forcing the nonlinear systems to perform and behave like linear systems, thus limiting its maximum potential. In this paper a novel nonlinear control design methodology is introduced that overcomes this limitation.
Several of the popular advanced nonlinear control system approaches are based in passivity and dissipative control theories. Initially, P. J. Moylan, Implications of Passivity in a Class of Nonlinear Systems, IEEE Transactions of Automatic Control, Vol. AC-19, No. 4, August 1974, pp. 373-381, discussed the implications of passivity for a broad class of nonlinear systems, wherein a connection is established between the input-output property of passivity and a set of constraints on the state equations for the system. Later, J. L. Wyatt, Jr., L. O. Chua, J. W. Gannett, I. C. Goknar, and D. N. Green, Energy Concepts in the State-Space Theory of Nonlinear n-Ports: Part I—Passivity, IEEE Transactions on Circuits and Systems, Vol. CAS-28, No. 1, January 1981, pp. 48-61; and J. L. Wyatt, Jr., L. O. Chua, J. W. Gannett, I. C. Goknar, and D. N. Green, Energy Concepts in the State-Space Theory of Nonlinear n-Ports: Part II—Losslessness, IEEE Transactions on Circuits and Systems, Vol. CAS-29, No. 7, July 1982, pp. 417-430, clarified the meaning of passivity and losslessness as understood in nonlinear circuit theory, and their counterparts in classical physics. Most recently, R. Ortega, Z. P. Jiang, and D. J. Hill, Passivity-Based Control of Nonlinear systems: A Tutorial, Proceedings of the American Control Conference, Albuquerque, N. Mex., June 1997, pp. 2633-237, reviewed recent results on the stabilization of nonlinear systems using a passivity approach. Passivity properties play a vital role in designing asymptotically stabilizing controllers for nonlinear systems where the nonlinear versions of the Kalman-Yacubovitch-Popov lemma are used as key testing tools. The dissipative characteristics of dynamical systems have their origins in work by J. C. Willems, Dissipative Dynamical Systems Part I: General Theory; Part II: Linear Systems with Quadratic Supply Rates, Archive for Rational Mechanics and Analysis, Vol. 45, pp. 321-393, 1972, with further specifics given by D. Hill and P. J. Moylan, The Stability of Nonlinear Dissipative Systems, IEEE Transactions on Automatic Control, October 1976, pp. 708-710, in which a technique is introduced for generating Lyapunov functions for a broad class of nonlinear systems represented by state equations. The system, for which a Lyapunov function is required, is assumed to have a property called dissipativeness. In other words, the system absorbs more energy from the external world than it supplies. Different types of dissipativeness can be considered depending on how the “power input” is selected. Dissipativeness is shown to be characterized by the existence of a computable function which can be interpreted as the “stored energy” of the system. Under certain conditions, this energy function is a Lyapunov function which establishes stability, and in some cases asymptotic stability, of the isolated system. It was shown that for a certain class of nonlinear systems, that an “energy” approach was useful in analyzing stability. P. Kokotovic and M. Arcak, Constructive Nonlinear Control: A Historical Perspective, Preprint submitted to Elsevier, August 2000, provide a recent discussion about the historical perspective of constructive nonlinear control theories. Structural properties of nonlinear systems and passivation-based designs exploit the connections between passivity and inverse optimality, and between Lyapunov functions and optimal value functions. Recursive design procedures, such as backstepping and forwarding, achieve certain optimal properties for important classes of nonlinear systems. Some of the more popular nonlinear control system designs, e.g., J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Inc., N.J., 1991; M. Kristic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, Inc., New York, 1995; and P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, Englewood Cliffs, N.J., 1996, have their fundamental foundations built upon these concepts.
In other engineering disciplines, A. A. Alonso and B. E. Ydstie, Stabilization of Distributed Systems Using Irreversible Thermodynamics, Automatica, Vol. 37, 2001, pp. 1739-1755, connect thermodynamics and the passivity theory of nonlinear control. The storage function is derived from the convexity of the entropy and is closely related to thermodynamic availability. Dissipation is related to positive entropy production. In this form the supply function is a product of force and flow variation variables. Results are discussed in relationship to heat conduction and reaction diffusion equation problems. K.-H. Anthony, Hamilton's Action Principle and Thermodynamics of Irreversible Processes—A Unifying Procedure for Reversible and Irreversible Processes, J. Non-Newtonian Fluid Mechanics, Vol. 96, 2001, pp. 291-339, suggests that non-equilibrium thermodynamics of irreversible processes may be included into the framework of a Lagrangian formalism. This formalism presents a unified method for reversible and irreversible processes. A straightforward procedure allows for the incorporation of both the first and second laws of thermodynamics into the Lagrangian. The theory is illustrated in three representative examples which include; material flow, heat conduction, diffusion and chemical reactions.
The main contribution of this paper is to present a novel nonlinear control design methodology that is based on thermodynamic exergy and irreversible entropy production concepts. Relationships are developed between exergy, irreversible entropy production, Hamiltonian systems, Lyapunov optimal functions, electric AC power concepts, and power flow, for control system design. Both necessary and sufficient conditions for stability are determined for nonlinear systems. By combining the first and second laws of thermodynamics, an exergy analysis approach is developed to construct Lyapunov optimal functions for Hamiltonian systems. The first time derivative of the Lyapunov functions, based on exergy, irreversible entropy production rate, and power flow is partitioned into either exergy dissipative or exergy generative terms.
Embodiments of the present invention are also described in Robinett, et al., “Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control System Design: Robotic Servo Applications”, Proceedings of the 2006 IEEE International Conference on Robotics and Automation, pp. 3685-3692, May 2006; Robinett, et al., “Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control System Design: Regulators”, Proceedings of the 2006 IEEE International Conference on Control Applications, pp. 2249-2256, October 2006; and Robinett, et al., “Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control System Design: Nonlinear Systems”, Proceedings of the 2006 14th Mediterranean Conference on Control and Automation, pp. 1-8 (June 2006); Robinett III, R. D., Wilson, D. G. and Reed, A. W., “Exergy Sustainability for Complex Systems”, InterJournal Complex Systems, 1616, New England Complex Systems Institute, September 2006; Robinett III, R. D. and Wilson, D. G., “Decentralized Exergy/Entropy Thermodynamic Control for Collective Robotic Systems”, ASME 2007 International Mechanical Engineering Congress & Exposition, Seattle, Wash., Nov. 11-15, 2007; Robinett, III, R. D. and Wilson, D. G., “Collective Plume Tracing: A Minimal Information Approach to Collective Control,” IEEE 2007 American Control Conference, New York, N.Y., July 2007; Robinett III, R. D. and Wilson, D. G., “Exergy and Entropy Thermodynamic Concepts for Nonlinear Control Design”, 2006 ASME International Mechanical Engineering Congress & Exposition, Chicago, Ill., Nov. 5-10, 2006; Robinett III, R. D. and Wilson, D. G., “Exergy and Entropy Thermodynamic Concepts for Control System Design: Slewing Single Axis”, 2006 AIAA Guidance, Navigation, and Control Conference, Keystone, Colo., Aug. 21-24, 2006; Robinett III, R. D. and Wilson, D. G., “Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control Design: Nonlinear Systems”, 14th Mediterranean Conference on Control and Automation, Ancona, Italy, Jun. 28-30, 2006; Robinett III, R. D. and Wilson, D. G., “Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control Design: Nonlinear Regulator Systems”, The 8th IASTED International Conference on Control and Applications, Montreal, Quebec, Canada, May 24-26, 2006; Robinett III, R. D., Wilson, D. G., and Reed, A. W., “Exergy Sustainability”, Sandia Report SAND2006-2759, May 2006; and Robinett III, R. D. and Wilson, D. G., “Collective Systems: Physical and Information Exergies”, Sandia Report SAND2007-2327, April 2007, all of which are incorporated herein by reference.